The basic rule, which you probably know, is that there is a well-defined list of verbs that are followed by to-infinitive, like "want" and "need". All the others (including "hear") are followed by -ing. e.g. I heard shouting in the distance but I don't know who was shouting. With the verbs "hear" and "see", we can also add an object person that acts as the object of "hear" and the subject of the -ing (gerund) e.g. I heard someone shouting in the distance. In these sentences, the meaning is physical. My ears detected these noises. You would not reformulate them as sentences starting "I heard that...." This is because "I heard that" has a different meaning. It means "I heard some words that made me intellectually aware of some information." The examples of Teacher Jan and Mike relate to this sense of "hear". At your level, you need to know all three verb structures that I've mentioned in this answer.

This can be a very complicated subject. The word 'hear' is most often followed by a noun or pronoun (object) rather than a verb. Examples: I hear (that) Stephanie passed her exam. I hear (that) you're leaving town today. I hear (that) rain is expected this afternoon. I can't think of any example of using 'hear' with another verb (to-infinitve or bare infinitive) that would make any sense.

I think it would always be to + inf. I hear to be successful around here the boss has to like you. I hear to learn a new language takes ages. I can't think of any examples without to.. It would have to be 'I hear learning a new language..'